If ${log}_{3} {5 + 4 {log}_{3} (x - 1)} = 2$ , then $x$ is equal to

2

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4

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8

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{log}_{2} 16

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Solution

The correct options are
C $4$
D ${log}_{2} 16$
${log}_{3} {5 + 4 {log}_{3} (x - 1)} = 2 \Rightarrow 5 + 4 {log}_{3} (x - 1) = 3^{2} \Rightarrow {log}_{3} (x - 1) = 1 \Rightarrow x - 1 = 3 \Rightarrow x = 4$
Which can be written as $x = 4 = 4 {log}_{2} 2 [∵ {log}_{a} a = 1] = {log}_{2} 2^{4} = {log}_{2} 16$
Ans: B, D

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